[JRTJH]

If it's "cycling on and off in greater than 100F temperatures" I'd first think of two possibilities:

1. It's at the upper limit of what it can do and as the compressor temperature rises, the thermal protection cuts in to shut the compressor off to protect it from over heating...

2. It's a control system/thermostat issue. On some newer trailers with the control box in the rooftop unit and controlled by the In-Command system, there is/was an issue where the system would fail to start if the ambient temps were below 40F or above 100F. Once the system is turned on and operating, I'm not aware of a "ambient temp issue" but I also haven't heard of anyone "operating their air conditioner and experiencing inadequate cooling that allows the system to rise above that "system limitation issue", so you might be the "first to see those conditions....

At any rate, if the system is shutting down at temps above 100F, then there's a problem and you need to have it addressed. It may be that simply the A/C is too small to keep up or it could be a control/thermostat issue or it could be a low freon charge or even an evaporator/condensor cooling fin blockage.